Kelly e/w

Van Dice

Question about the Kelly Criterion and e/w betting.
The Kelly Criterion itslef is fairly simple and easy to use, I'm just not quite sure how to apply it when betting e/w.

I will estimate different edges for the win and place parts of the bet, but obviously I am limited to the same stake for each. How do I adjust the formula to find the optimal stake? Can anyone direct me to where this has been discussed, or if anyone uses it themselves I'd appreciate advice.

Thanks

HiCloy

Interesting question

Don't mean to be smart but bet on betfair or similar and you can adjust your stake for the win and place part.

A drawback of this is that this would take the bets as independent when they are clearly not. The correlation of the win and place part of the bet is not neccessarily constant ie if a horse is 4/1 and has a 20% chance of winning they do not automatically have a 50% chance of being placed as a standard bookies 1/4 odds the place would suggest

I came across this before for analysing multiscenario bets such as this.

http://www.cisiova.com/betsizing.asp

Taking the example of the horse at 4/1 who you are backing each way. If the odds were fair then

P(win) = 0.2, ROI(win) = +250%
P(Place, not winning) = 0.3, ROI(win) = 0
Prob(Unplaced) = 0.5, ROI(win) = -100%

So EV = 0

Say as in a common racing scenario the place odds represent good value, maybe if there's a hot favourite and the rest of the field is poor. You may think

P(win) = 0.2
P(place, not win) = 0.4
P(Unplaced) = 0.4
same ROI as before
So EV = +10%

Plugging these probabilites into the page above gives a Kelly percentage of 6.7%.

The general formula behind the question is given on the page, but it admits an optimization technique (read solver for Excel!) is used to calculate the exact result

Van Dice

That seems to be exactly what I was looking for, thanks HiCloy. New toys like this = early Christmas